A single molecule has a mass of 7.31 ×10^-23 g . Provide an example of a real molecule that can

step 1 Chapter 1, Problem 71, tells us that a single molecule has a mass of 7 .31 times 10 to the negat

A single molecule has a mass of 7.31 ×10^-23 g . Provide an...

A single molecule has a mass of $7.31 \times 10^{-23} \mathrm{~g} .$ Provide an example of a real molecule that can have this mass. Assume the elements that make up the molecule are made of light isotopes where the number of protons equals the number of neutrons in the nucleus of each element.

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental constant (approximately 6.022 x 10^23) that defines the number of constituent particles, usually atoms or molecules, in one mole of a substance. It serves as the conversion factor between the macroscopic scale (molar mass) and the microscopic scale (mass of a single molecule). This concept is used to determine the mass of one molecule from the known molar mass of a substance.

Calculating Mass of a Single Molecule

This concept involves the conversion process where the molar mass of a substance (calculated based on the atomic masses of its constituent elements) is divided by Avogadro's number to yield the mass of an individual molecule. In practice, if the calculated single molecule mass matches the mass given in the problem, it suggests that the candidate molecule, such as carbon dioxide (CO?) with a molar mass of approximately 44 g/mol, is a valid example.

Atomic Structure and Isotopes

This concept involves understanding that atoms are composed of protons, neutrons, and electrons. In particular, isotopes of an element have the same number of protons but different numbers of neutrons. For molecules made from light isotopes, as specified in the question, the number of neutrons is equal to the number of protons. This specification is important in accurately determining the atomic masses that contribute to a molecule's overall mass.

Molecular Mass and Molar Mass

Molecular mass is the sum of the masses of all the atoms in a molecule, usually expressed in unified atomic mass units (u), while molar mass is the mass of one mole of a substance expressed in grams per mole. The link between the two lies in the fact that the mass of a single molecule can be calculated by dividing the molar mass by Avogadro's number. This relationship is crucial when trying to match a given single molecule mass to a candidate molecule.

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